Capacity Of Pipeline Calculation

Poiseuille's Law:

\[ Q = \frac{\pi \times ID^4 \times \Delta P}{128 \times \mu \times L} \]

Inner Diameter (ID):

Pressure Difference (ΔP):

Dynamic Viscosity (μ):

Pa·s

Length (L):

Flow Capacity (Q):

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1. What is Poiseuille's Law?

Poiseuille's Law describes the flow capacity of a fluid through a cylindrical pipe under laminar flow conditions. It provides a mathematical relationship between flow rate, pipe dimensions, fluid properties, and pressure difference.

2. How Does the Calculator Work?

The calculator uses Poiseuille's Law equation:

\[ Q = \frac{\pi \times ID^4 \times \Delta P}{128 \times \mu \times L} \]

Where:

\( Q \) — Flow capacity (m³/s)
\( ID \) — Inner diameter of the pipe (m)
\( \Delta P \) — Pressure difference along the pipe (Pa)
\( \mu \) — Dynamic viscosity of the fluid (Pa·s)
\( L \) — Length of the pipe (m)

Explanation: The equation shows that flow rate is proportional to the fourth power of the pipe diameter and the pressure difference, and inversely proportional to the fluid viscosity and pipe length.

3. Importance of Flow Capacity Calculation

Details: Accurate flow capacity calculation is crucial for pipeline design, fluid transport systems, hydraulic engineering, and various industrial applications involving fluid flow.

4. Using the Calculator

Tips: Enter inner diameter in meters, pressure difference in Pascals, dynamic viscosity in Pa·s, and length in meters. All values must be positive and non-zero.

5. Frequently Asked Questions (FAQ)

Q1: What are the limitations of Poiseuille's Law?
A: Poiseuille's Law applies only to laminar flow, Newtonian fluids, and straight circular pipes with constant cross-section.

Q2: How does pipe diameter affect flow capacity?
A: Flow capacity increases with the fourth power of the diameter, meaning doubling the diameter increases flow capacity by 16 times.

Q3: What is considered laminar flow?
A: Laminar flow typically occurs at Reynolds numbers below 2000, where fluid flows in parallel layers with no disruption between them.

Q4: How does viscosity affect flow capacity?
A: Higher viscosity fluids have lower flow capacity as viscosity appears in the denominator of the equation.

Q5: Can this calculator be used for turbulent flow?
A: No, Poiseuille's Law is specifically for laminar flow. Different equations are needed for turbulent flow conditions.